Answer:
b = - 0.432
Step-by-step explanation:
It takes 200 seconds to produce the first widget. And by the 400th widget, it takes only 15 seconds.
Now, the formula that gives the time to make the nth widget is given by
[tex]T_{n} = T_{1} (n)^{b}[/tex] and we have to evaluate the constant b from the above-given conditions.
So, [tex]15 = 200(400)^{b}[/tex]
⇒ [tex]400^{b} = 0.075[/tex]
Taking log on both sides
b log (400) = log (0.075)
⇒ b = - 0.432 (Answer)
